Abstract Solvent stress cracking studies have been carried out in o-xylene and other solvents on polyetherimide-based materials including neat resin, woven fabric composites, and adhesively bonded systems. The results show crack growth in solvents at very low G(I) levels as compared with tests in air. The composite and adhesively bonded systems have sufficiently high residual thermal stresses to drive an array of intersecting matrix/adhesive cracks even without mechanical loading. The matrix/adhesive residual stress-driven crack patterns retard main delamination crack growth relative to that in the neat resin, and raise the applied threshold G(I) level for main crack growth by about a factor of 10. Stress-corrosion cracking in a commercially available, hot isostatically pressed (HIPed), yttria-fluxed, silicon nitride was the prevalent mode of failure in specimens creep-ruptured at 1,370 C. High-temperature diffusional processes associated with oxygen were responsible for the creation of an advancing stress-corrosion front that had formed at the specimen surface and advanced radially inward. The volume of material in the wake of the stress-corrosion front possessed a high concentration of lenticular cavities at two-grain boundaries, a high concentration of multigrain junction cavities, and large amorphous ``pockets`` in other multigrain junctions that were abnormally rich in oxygen and yttrium.

Protel for windows 10. The combination of tensile stress and the high concentration of cavities in the near-surface volume of the material resulted in microcrack coalescence or the formation of a planar, stress-corrosion crack. The concurrent growth of the stress-corrosion front and crack during the tensile creep-rupture tests ultimately led to stress-induced failure.

Aug 1, 2018 - We thus observe that viscoelastic effects are important for parallel fractures. Very close to the tip (l ≪ R), the shape merges to a lenticular form [8]. The cracks in the y−zplane and the x−zplane are called a.

Lenticular Effects 4 1 Cracker Barrel

Santee Cooper (South Carolina Public Service Authority) experienced twenty-three tube failures in a high pressure feedwater heater that was in service less than three years. The tube failures were located at baffles adjacent to both exists of the dual flow desuperheater. Metallurgical analysis of the failed tubes indicated that stress corrosion cracking of the 304N stainless steel was the primary failure mode (Rudin, 1994; Shifler, 1994). Denoiser serial number cracked tongue. The investigation to determine the factors leading to the onset of stress corrosion cracking included analysis of heater acceptance tests, the heater manufacturer`s proposal and manufacturing procedures, operational data, eddy current reports, metallurgical reports, and a heater design review for vibration and wet wall potential (formation of condensation on the outside diameter (OD) of the tube prior to the desuperheater exit). Ceramic matrix composites are being developed to operate at elevated temperatures and in oxidizing environments. Considerable improvements are being made in the creep resistance of SiC fibers and hence in the high-temperature properties of SiCf/SiC composites; however, more needs to be known about the stability of these materials in oxidizing environments before they will be widely accepted. Experimental weight change (1,2) and crack growth data (3,4) supports the conclusion that O2 enhanced crack growth of SiCf/SiC occurs by more than one mechanism depending on the experimental conditions.

The dimensions are shown in Fig. The crack on each specimen was made as follows: a line-incisor with a radius of 0.1 mm was used to make an initiatory crack and then a sharp razor was used to make the crack tip. The radius of the razor was approximately 25 μm. The validity of this pre-cracking method has been justified by Pardoen et al. Investigating the process of lenticular image creation with the animation effect.

A lenticular lens is an array of lenses, designed so that when viewed from slightly different angles, different parts of the image underneath is shown.^{[1][2][failed verification – see discussion]} The most common example is the lenses used in lenticular printing, where the technology is used to give an illusion of depth, or to make images that appear to change or move as the image is viewed from different angles.

Applications[edit]

Lenticular printing[edit]

Lenticular printing is a multi-step process consisting of creating a lenticular image from at least two existing images, and combining it with a lenticular lens. This process can be used to create various frames of animation (for a motion effect), offsetting the various layers at different increments (for a 3D effect), or simply to show a set of alternate images which may appear to transform into each other.

Corrective lenses[edit]

Lenticular lenses are sometimes used as corrective lenses for improving vision. A bifocal lens could be considered a simple example.

Lenticular eyeglass lenses have been employed to correct extreme hyperopia (farsightedness), a condition often created by cataract surgery when lens implants are not possible. To limit the great thickness and weight that such high-power lenses would otherwise require, all the power of the lens is concentrated in a small area in the center. In appearance, such a lens is often described as resembling a fried egg: a hemisphere atop a flat surface. The flat surface or 'carrier lens' has little or no power and is there merely to fill up the rest of the eyeglass frame and to hold or 'carry' the lenticular portion of the lens. This portion is typically 40 mm (1.6 in) in diameter but may be smaller, as little as 20 mm (0.79 in), in sufficiently high powers. These lenses are generally used for plus (hyperopic) corrections at about 12 diopters or higher. A similar sort of eyeglass lens is the myodisc, sometimes termed a minus lenticular lens, used for very high negative (myopic) corrections. More aesthetic aspheric lens designs are sometimes fitted.^[3] A film made of cylindrical lenses molded in a plastic substrate as shown in above picture, can be applied to the inside of standard glasses to correct for diplopia. The film is typically applied to the eye with the good muscle control of direction. Diplopia (also known as double vision) is typically caused by a sixth cranial nerve palsy that prevents full control of the muscles that control the direction the eye is pointed in. These films are defined in the number of degrees of correction that is needed where the higher the degree, the higher the directive correction that is needed.

Lenticular screens[edit]

Screens with a molded lenticular surface are frequently used with projection television systems. In this case, the purpose of the lenses is to focus more of the light into a horizontal beam and allow less of the light to escape above and below the plane of the viewer. In this way, the apparent brightness of the image is increased.

Ordinary front-projection screens can also be described as lenticular. In this case, rather than transparent lenses, the shapes formed are tiny curved reflectors. Lenticular screens are most often used for Ambient Light Rejecting projector screens for Ultra Short Throw projectors.^[4] The lenticular structure of the surface reflects the light from the projector to the viewer without reflecting the light from sources above the screen.

3D television[edit]

As of 2010, a number of manufacturers were developing auto-stereoscopic high definition 3D televisions, using lenticular lens systems to avoid the need for special spectacles. One of these, Chinese manufacturer TCL, was selling a 42-inch (110 cm) LCD model—the TD-42F—in China for around US$20,000.^[5]

In 2021 only specialist manufacturers such as 'Looking Glass Factory' are making these kinds of display^[6]

Lenticular color motion picture processes[edit]

Lenticular lenses were used in early color motion picture processes of the 1920s such as the Keller-Dorian system and Kodacolor. This enabled color pictures with the use of merely monochrome film stock.^[7]

Angle of view of a lenticular print[edit]

The angle of view of a lenticular print is the range of angles within which the observer can see the entire image. This is determined by the maximum angle at which a ray can leave the image through the correct lenticule.

Angle within the lens[edit]

The diagram at right shows in green the most extreme ray within the lenticular lens that will be refracted correctly by the lens. This ray leaves one edge of an image strip (at the lower right) and exits through the opposite edge of the corresponding lenticule.

Lenticular Effects 4 1 Crackers

Definitions[edit]

• ${\displaystyle R}$ is the angle between the extreme ray and the normal at the point where it exits the lens,
• ${\displaystyle p}$ is the pitch, or width of each lenticular cell,
• ${\displaystyle r}$ is the radius of curvature of the lenticule,
• ${\displaystyle e}$ is the thickness of the lenticular lens
• ${\displaystyle h}$ is the thickness of the substrate below the curved surface of the lens, and
• ${\displaystyle n}$ is the lens's index of refraction.

Calculation[edit]

${\displaystyle R=A-\arctan \left(\frac{p}{h}\right)}$,

where

${\displaystyle A=\arcsin \left(\frac{p}{2r}\right)}$,

${\displaystyle h=e-f}$ is the distance from the back of the grating to the edge of the lenticule, and

${\displaystyle f=r-\sqrt{r^2-{\left(\frac{p}{2}\right)}^2}}$.

Angle outside the lens[edit]

The angle outside the lens is given by refraction of the ray determined above. The full angle of observation ${\displaystyle O}$ is given by

${\displaystyle O=2(A-I)}$,

where ${\displaystyle I}$ is the angle between the extreme ray and the normal outside the lens. From Snell's Law,

${\displaystyle I=\arcsin \left(\frac{n\sin (R)}{n_a}\right)}$,

where ${\displaystyle n_a\approx 1.003}$ is the index of refraction of air.

Example[edit]

Consider a lenticular print that has lenses with 336.65 µm pitch, 190.5 µm radius of curvature, 457 µm thickness, and an index of refraction of 1.557. The full angle of observation ${\displaystyle O}$ would be 64.6°.

Rear focal plane of a lenticular network[edit]

The focal length of the lens is calculated from the lensmaker's equation, which in this case simplifies to:

${\displaystyle F=\frac{r}{n-1}}$,

where ${\displaystyle F}$ is the focal length of the lens.

The back focal plane is located at a distance ${\displaystyle BFD}$ from the back of the lens:

${\displaystyle BFD=F-\frac{e}{n}.}$

A negative BFD indicates that the focal plane lies inside the lens.

In most cases, lenticular lenses are designed to have the rear focal plane coincide with the back plane of the lens. The condition for this coincidence is ${\displaystyle BFD=0}$, or

${\displaystyle e=\frac{nr}{n-1}.}$

This equation imposes a relation between the lens thickness ${\displaystyle e}$ and its radius of curvature ${\displaystyle r}$.

Example[edit]

The lenticular lens in the example above has focal length 342 µm and back focal distance 48 µm, indicating that the focal plane of the lens falls 48 micrometers behind the image printed on the back of the lens.

See also[edit]

• Fresnel lens, a different 'flat' lens technology

References[edit]

1. ^'Lenticular, how it works'. Lenstar.org. Archived from the original on 3 May 2016. Retrieved 25 May 2017.
2. ^DIY Printed Holographic Display (Lenticular Optics Explained), retrieved 8 May 2021
3. ^Jalie, Mo (2003). Ophthalmic Lenses and Dispensing. Elsevier Health Sciences. p. 178. ISBN0-7506-5526-7.
4. ^'Lenticular Projector Screen Vs. Fresnel Projector Screen for Ultra Short Throws'. ProjectorScreen.com. Retrieved 10 February 2021.
5. ^'Give Me 3D TV, Without The Glasses'. Archived from the original on 13 February 2010. Retrieved 6 May 2010.
6. ^Factory, Looking Glass. 'Looking Glass Factory · The World's Leading Holographic Display'. Looking Glass Factory · The World's Leading Holographic Display. Retrieved 8 May 2021.
7. ^'Lenticular films on Timeline of Historical Film Colors'. Archived from the original on 9 July 2014. Retrieved 29 June 2014.

• Bartholdi, Paul (1997). 'Quelques notions d'optique' (in French). Observatoire de Genève. Retrieved 19 December 2007.
• Soulier, Bernard (2002). 'Principe de fonctionnement de l'optique lenticulaire' (in French). Séquence 3d. Retrieved 22 December 2007.
• Okoshi, Takanori Three-Dimensional Imaging Techniques Atara Press (2011), ISBN978-0-9822251-4-1.

External links[edit]

• Lecture slides covering lenticular lenses (PowerPoint) by John Canny